DIsplace Modifier Problem
My original UV image had a middle stripe of a blend of the two colored sides creating an illusion of two colors mixing in Blender. 
I recreated the UV image with no stripe. It's working now. Also, I recreated a plane mesh, and instead of subdividing it a lot as I had originally tried, I used a ton of loop cuts in the axis of distortion (y), and then another loop cut perpendicular to that (x) and marked as seam to bisect the plane.

https://gph.is/2Dh8vDE